# yI1-xI1-EMWproposal.R
# Philips, Andrew Q. "How to Avoid Incorrect Inference (While Gaining Correct Ones) in Dynamic Models". Forthcoming at Political Science Research and Methods. 
# andrew.philips@colorado.edu
# 2/9/21
#
# Figures produced in this R script:
#   --SI, Figure 33: "yi1-xi1-LRlxYES-EMWproposal.pdf"
# -----------------------------------
# -----------------------------------
# EXPERIMENT 4: Y ~ I(1), X ~ I(1)
# Type I error
# ONLY CALCULATING THE LRE IF L.X (ARDL/ECM) AND X (LDV) ARE FIRST STAT SIG (to appear in SI, Section 2)
# -----------------------------------
rm(list = ls())
setwd("~/Dropbox/My_Folder/Papers-Projects/Wlezien-Enns-PSRM/Final-Feb2021/scripts/")
# -----------------------------------
library(dynamac)
library(nlWaldTest)
library(ggplot2)
library(grid)
library(gridExtra)
library(dplyr)

set.seed(8349809)
# -------------------------------------------------------------
# EXPERIMENT 4: Y ~ I(1), X ~ I(1)
sims = 2000 # no. sims
N <- c(50, 250, 1000) # number of obs
e.var <-  1 #c(1, 5) # error variance (in this case, variance in Y)

container.ardl <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 9) # null matrix to hold output
# cols = sims, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var
container.ecm <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 9) # null matrix to hold output
# cols = sims, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var
container.ldv <- matrix(NA, nrow = sims*length(N)*length(e.var), ncol = 9) # null matrix to hold output
# cols = sims, N, Beta.x, UL.beta.x, LL.beta.x, e.var
# -------------------------------------------------------------

row <- 1
prog <- txtProgressBar(min = 0, max = sims, style = 3)
for (s in 1:sims) {
  for (n in N) {
    for (ev in e.var) {
      setTxtProgressBar(prog, value = s)
      # create Y
      y <- cumsum(rnorm(n + 100, sd = sqrt(ev)))
      # create X
      x <- cumsum(rnorm(n + 100, sd = 1))
      # ARDL model:
      res.ardl <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)] + lshift(x, 1)[101:length(x)])
      # ECM model:
      res.ecm <- lm(dshift(y)[101:length(y)] ~ lshift(y, 1)[101:length(y)] + dshift(x)[101:length(x)] + lshift(x, 1)[101:length(x)])
      # LDV model
      res.ldv <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)])
      # static model
      res.static <- lm(y[101:length(y)] ~ x[101:length(x)])
      
      # grab QOI (FORALL): ----
      container.ardl[row, 1] <- container.ecm[row, 1] <- container.ldv[row, 1] <- s
      container.ardl[row, 2] <- container.ecm[row, 2] <- container.ldv[row, 2] <- n
      container.ardl[row, 9] <- container.ecm[row, 9] <- container.ldv[row, 9] <- ev
      
      # QOI (ARDL)
      container.ardl[row, 3] <- coef(res.ardl)[4] # beta.x
      container.ardl[row, 4] <- confint.default(res.ardl, parm = c(4), level = 0.95)[2] # UL
      container.ardl[row, 5] <- confint.default(res.ardl, parm = c(4), level = 0.95)[1] # LL
      # LR effects (ARDL)
      lrm <- nlConfint(res.ardl, "(a[3] + a[4])/(1-a[2])", level = 0.95)
      container.ardl[row, 6] <- lrm[1] # LRM
      container.ardl[row, 7] <- lrm[3] # LRM UL
      container.ardl[row, 8] <- lrm[2] # LRM LL
      
      # QOI (ECM)
      container.ecm[row, 3] <- coef(res.ecm)[4] # beta.d.x
      container.ecm[row, 4] <- confint.default(res.ecm, parm = c(4), level = 0.95)[2] # UL
      container.ecm[row, 5] <- confint.default(res.ecm, parm = c(4), level = 0.95)[1] # LL
      # LR effects (ECM)
      lrm <- nlConfint(res.ecm, "(a[4])/(-a[2])", level = 0.95)
      container.ecm[row, 6] <- lrm[1] # LRM
      container.ecm[row, 7] <- lrm[3] # LRM UL
      container.ecm[row, 8] <- lrm[2] # LRM LL
      
      # QOI (LDV)
      container.ldv[row, 3] <- coef(res.ldv)[3]
      container.ldv[row, 4] <- confint.default(res.ldv, parm = c(3), level = 0.95)[2] # UL
      container.ldv[row, 5] <- confint.default(res.ldv, parm = c(3), level = 0.95)[1] # LL
      # LR effects (LDV)
      lrm <- nlConfint(res.ldv, "(a[3])/(1-a[2])", level = 0.95)
      container.ldv[row, 6] <- lrm[1] # LRM
      container.ldv[row, 7] <- lrm[3] # LRM UL
      container.ldv[row, 8] <- lrm[2] # LRM LL
      
      row <- row + 1
    } # close error var loop
  } # close N loop
} # close sim loop

#save.image("scenario-yi1-xi1-EMWproposal-data.RData")
#load("scenario-yi1-xi1-EMWproposal-data.RData")

# Create rejection rates and label:
container.ardl <- as.data.frame(container.ardl)
# cols = sim, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ardl) <- c("sims", "Time", "Beta.lx", "Beta.lx.ul", "Beta.lx.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.ecm <- as.data.frame(container.ecm)
# cols = sim, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ecm) <- c("sims", "Time", "Beta.lx", "Beta.lx.ul", "Beta.lx.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")
container.ldv <- as.data.frame(container.ldv)
# cols = sim, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var
colnames(container.ldv) <- c("sims", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var")

# proportion false rejection
container.ardl$reject.beta.lx <- ifelse(container.ardl$Beta.lx.ll > 0 | container.ardl$Beta.lx.ul < 0, 1, 0)
container.ecm$reject.beta.lx <- ifelse(container.ecm$Beta.lx.ll > 0 | container.ecm$Beta.lx.ul < 0, 1, 0)
container.ldv$reject.beta.x <- ifelse(container.ldv$Beta.x.ll > 0 | container.ldv$Beta.x.ul < 0, 1, 0)

# coverage of LRM:
container.ardl$reject.lrm <- ifelse(container.ardl$LR.x.LL > 0 | container.ardl$LR.x.UL < 0, 1, 0)
container.ecm$reject.lrm <- ifelse(container.ecm$LR.x.LL > 0 | container.ecm$LR.x.UL < 0, 1, 0)
container.ldv$reject.lrm <- ifelse(container.ldv$LR.x.LL > 0 | container.ldv$LR.x.UL < 0, 1, 0)

# Coding of rejection of LRM:
# = 1 if we reject LRM AND also reject beta.lx/beta.x, 0 otherwise
container.ardl$reject.lrm.yes.lx <- ifelse(container.ardl$reject.lrm == 1 & container.ardl$reject.beta.lx == 1, 1, 0)
container.ecm$reject.lrm.yes.lx <- ifelse(container.ecm$reject.lrm == 1 & container.ecm$reject.beta.lx == 1, 1, 0)
container.ldv$reject.lrm.yes.x <- ifelse(container.ldv$reject.lrm == 1 & container.ldv$reject.beta.x == 1, 1, 0)

# = 1 if we reject LRM AND NOT reject beta.lx/beta.x, 0 otherwise
container.ardl$reject.lrm.no.lx <- ifelse(container.ardl$reject.lrm == 1 & container.ardl$reject.beta.lx == 0, 1, 0)
container.ecm$reject.lrm.no.lx <- ifelse(container.ecm$reject.lrm == 1 & container.ecm$reject.beta.lx == 0, 1, 0)
container.ldv$reject.lrm.no.x <- ifelse(container.ldv$reject.lrm == 1 & container.ldv$reject.beta.x == 0, 1, 0)

# collapse everything down:
container.collapse.ardl <- container.ardl %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.lx = mean(reject.beta.lx),
            reject.lrm = mean(reject.lrm),
            reject.lrm.yes.lx = mean(reject.lrm.yes.lx),
            reject.lrm.no.lx = mean(reject.lrm.no.lx))

container.collapse.ecm <- container.ecm %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.lx = mean(reject.beta.lx),
            reject.lrm = mean(reject.lrm),
            reject.lrm.yes.lx = mean(reject.lrm.yes.lx),
            reject.lrm.no.lx = mean(reject.lrm.no.lx))

container.collapse.ldv <- container.ldv %>%
  group_by(Time, e.var) %>%
  summarize(reject.beta.x = mean(reject.beta.x), 
            reject.lrm = mean(reject.lrm),
            reject.lrm.yes.lx = mean(reject.lrm.yes.x), # need to label this as lx for appending, even though it's x
            reject.lrm.no.x = mean(reject.lrm.no.x))

# need to combine all the model datasets since geom_bar doesn't work on separate datasets
container.collapse.ardl$model.type <- "ARDL"
container.collapse.ecm$model.type <- "ECM"
container.collapse.ldv$model.type <- "LDV"
# Create a appended long-run dataset
# long run: time (1), e.var (2), reject.lrm.yes.lx (5), modle type (7)
container.collapse.all.LR <- rbind(container.collapse.ardl[c(1,2,5,7)], container.collapse.ecm[c(1,2,5,7)], container.collapse.ldv[c(1,2,5,7)])
container.collapse.all.LR$Time <- as.factor(container.collapse.all.LR$Time)
container.collapse.all.LR$e.var <- as.factor(container.collapse.all.LR$e.var)

#  now create a geom_bar when error variance = 1:
p1 <- ggplot(data = subset(container.collapse.all.LR, e.var == 1), aes(x = model.type, y = reject.lrm.yes.lx, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") + geom_hline(yintercept = 0.05, color = "black", size = 1) + ylab("Proportion Rejected") + xlab("Model") + ggtitle("Long-Run") + scale_y_continuous(limits = c(0, 1))

pdf("yi1-xi1-LRlxYES-EMWproposal.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, ncol = 1)
dev.off()
